Calculate c <a, b>
15.21 Express c<a,b> in component form, assuming a, b, and c are real numbers.
The vector <a,b> is multiplied by a real number c; that real number is called a scalar. To multiply a vector in component form by a scalar value, multiply each of the components by the scalar. In this example, multiply both a and b by c.
A vector has a value (magnitude) and a direction. A scalar only has a value. However, that value changes the SCALE of the vector. For example, multiplying a vector by the scalar 2 doubles its length.
c<a,b> = <ca, cb>
15.22 Express the vector in component form: 3<4,7>.
Multiply each of the components of vector <4,7> by 3.
15.23 Express the vector in component form: –5<–1,8>.